Transcript of Advanced SynopticM. D. Eastin QG Analysis: System Evolution.
Slide 1
Advanced SynopticM. D. Eastin QG Analysis: System
Evolution
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Advanced SynopticM. D. Eastin QG Analysis QG Theory Basic Idea
Approximations and Validity QG Equations / Reference QG Analysis
Basic Idea Estimating Vertical Motion QG Omega Equation: Basic Form
QG Omega Equation: Relation to Jet Streaks QG Omega Equation:
Q-vector Form Estimating System Evolution QG Height Tendency
Equation Diabatic and Orographic Processes Evolution of Low-level
Cyclones Evolution of Upper-level Troughs
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Advanced SynopticM. D. Eastin Forecast Needs: The public
desires information regarding temperature, humidity, precipitation,
and wind speed and direction up to 7 days in advance across the
entire country Such information is largely a function of the
evolving synoptic weather patterns (i.e., surface pressure systems,
fronts, and jet streams) Forecast Method: Kinematic Approach:
Analyze current observations of wind, temperature, and moisture
fields Assume clouds and precipitation occur when there is upward
motion and an adequate supply of moisture QG theory QG Analysis:
Vertical Motion: Diagnose synoptic-scale vertical motion from the
observed distributions of differential geostrophic vorticity
advection and temperature advection System Evolution: Predict
changes in the local geopotential height patterns from the observed
distributions of geostrophic vorticity advection and differential
temperature advection QG Analysis: Basic Idea
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Advanced SynopticM. D. Eastin Recall: Two Prognostic Equations
Two Unknowns: We defined geopotential height tendency ( X ) and
then expressed geostrophic vorticity ( g ) and temperature (T) in
terms of the height tendency. QG Analysis: A Closed System of
Equations
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Advanced SynopticM. D. Eastin The QG Height Tendency Equation:
We can also derive a single prognostic equation for X by combining
our modified vorticity and thermodynamic equations (the
height-tendency versions): To do this, we need to eliminate the
vertical motion () from both equations Step 1: Apply the operator
to the thermodynamic equation Step 2:Multiply the vorticity
equation by Step 3:Add the results of Steps 1 and 2 After a lot of
math, we get the resulting prognostic equation QG Analysis: System
Evolution Vorticity Equation Adiabatic Thermodynamic Equation
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Advanced SynopticM. D. Eastin The QG Height Tendency Equation:
This is (2.32) in the Lackmann text This form of the equation is
not very intuitive since we transformed geostrophic vorticity and
temperature into terms of geopotential height. To make this
equation more intuitive, lets transform them back QG Analysis:
System Evolution
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term A Term B Term C To obtain an actual value for X (the
ideal goal), we would need to compute the forcing terms (Terms B
and C) from the three-dimensional wind and temperature fields, and
then invert the operator in Term A using a numerical procedure,
called successive over-relaxation, with appropriate boundary
conditions This is NOT a simple task (forecasters never do this)..
Rather, we can infer the sign and relative magnitude of X simple
inspection of the three-dimensional absolute geostrophic vorticity
and temperature fields (forecasters do this all the time) Thus,
lets examine the physical interpretation of each term. QG Analysis:
System Evolution
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term A Term B Term C Term A:Local Geopotential Height
Tendency This term is our goal a qualitative estimate of the
synoptic-scale geopotential height change at a particular location
For synoptic-scale atmospheric waves, this term is proportional to
X Thus, if we incorporate the negative sign into our physical
interpretation, we can just think of this term as local
geopotential height change QG Analysis: System Evolution
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term A Term B Term C Term B:Geostrophic Advection of
Absolute Vorticity (Vorticity Advection) Recall for a Single
Pressure Level: Positive vorticity advection (PVA)PVA causes local
vorticity increases From our relationship between g and , we know
that PVA is equivalent to: therefore: PVA or, since: PVA Thus, we
know that PVA at a single level leads to height falls Using similar
logic, NVA at a single level leads to height rises QG Analysis:
System Evolution
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term B:Geostrophic Advection of Absolute Vorticity
(Vorticity Advection) Trough Axis Initial Time NVA Expect Height
Rises PVA Expect Height Falls Expect the trough to move east
Initial Time QG Analysis: System Evolution Full-Physics Model
Analysis
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Advanced SynopticM. D. Eastin Trough Axis Initial Time 12 Hours
Later The BASIC QG Height Tendency Equation: Term B:Geostrophic
Advection of Absolute Vorticity (Vorticity Advection) QG Analysis:
System Evolution Generally consistent with expectations!
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term B:Geostrophic Advection of Absolute Vorticity
(Vorticity Advection) Generally ConsistentBUTRemember! Only
evaluated one level (500mb) should evaluate multiple levels Used
full wind and vorticity fields should use geostrophic wind and
vorticity Mesoscale-convective processes QG focuses on only
synoptic-scale (small R o ) Condensation / Evaporation neglected
diabatic processes Did not consider differential temperature
(thermal) advection (Term C)!!! Application Tips: Often the primary
forcing in the upper troposphere (500 mb and above) Term is equal
to zero at local vorticity maxima / minima If the vorticity maxima
/ minima are collocated with trough / ridge axes, (which is often
the case) this term cannot change system strength by increasing or
decreasing the amplitude of the trough / ridge system Thus, this
term is often responsible for system motion [more on this later] QG
Analysis: System Evolution
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term A Term B Term C Term C:Vertical Derivative of
Geostrophic Temperature Advection (Differential Thermal Advection)
Consider a three layer atmosphere where the warm air advection
(WAA) is strongest in the upper layer The greater temperature
increase aloft will produce the greatest thickness increase in the
upper layer and lower the pressure surfaces (or heights) in the
lower levels Therefore an increase in WAA advection with height
leads to height falls QG Analysis: System Evolution WAA Z-top
Z-400mb Z-700mb Z-bottom Z increases ZZ Height Falls occur below
the level of maximum WAA
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term A Term B Term C Term C:Vertical Derivative of
Geostrophic Temperature Advection (Differential Thermal Advection)
Possible height fall scenarios:Strong WAA in upper levels Weak WAA
in lower levels WAA in upper level CAA in lower levels No
temperature advection in upper levels CAA in lower levels Weak CAA
in upper levels Strong CAA in lower levels QG Analysis: System
Evolution
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term A Term B Term C Term C:Vertical Derivative of
Geostrophic Temperature Advection (Differential Thermal Advection)
Consider a three layer atmosphere where the warm air advection
(CAA) is strongest in the upper layer The greater temperature
increase aloft will produce the greatest thickness increase in the
upper layer and lower the pressure surfaces (or heights) in the
lower levels Therefore an increase in CAA advection with height
leads to height rises QG Analysis: System Evolution Height rises
occur below the level of maximum CAA Z-top Z-400mb Z-700mb Z-bottom
Z decreases ZZ
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term A Term B Term C Term C:Vertical Derivative of
Geostrophic Temperature Advection (Differential Thermal Advection)
Possible height rise scenarios:Strong CAA in upper levels Weak CAA
in lower levels CAA in upper level WAA in lower levels No
temperature advection in upper levels WAA in lower levels Weak WAA
in upper levels Strong WAA in lower levels QG Analysis: System
Evolution
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term C:Vertical Derivative of Geostrophic Temperature
Advection (Differential Thermal Advection) QG Analysis: System
Evolution Initial Trough Axis Strong WWA Weaker WAA aloft (not
shown) Expect Height Rises Initial Time 850 mb Strong CAA Weaker
CAA aloft (not shown) Expect Height Falls Full-Physics Model
Analysis
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Advanced SynopticM. D. Eastin Initial Trough Axis 12 Hours
Later 850 mb Trough deepened Ridge rose slightly The BASIC QG
Height Tendency Equation: Term C:Vertical Derivative of Geostrophic
Temperature Advection (Differential Thermal Advection) QG Analysis:
System Evolution Generally consistent with expectations!
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term C:Vertical Derivative of Geostrophic Temperature
Advection (Differential Thermal Advection) Generally
ConsistentBUTRemember! Used full wind field should use geostrophic
wind Only evaluated one level (850mb) should evaluate multiple
levels/layers ** Mesoscale-convective processes QG focuses on only
synoptic-scale (small R o ) Condensation / Evaporation neglected
diabatic processes Did not consider vorticity advection (Term B)!!!
Application Tips: Often the primary forcing in the lower
troposphere (below 500 mb) Term is equal to zero at local
temperature maxima / minima Since the temperature maxima / minima
are often located between the trough / ridge axes, significant
temperature advection (or height changes) can occur at the axes and
thus amplify the system intensity QG Analysis: System
Evolution
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term C:Vertical Derivative of Geostrophic Temperature
Advection (Differential Thermal Advection) Important: You should
evaluate the vertical structure of temperature advection!!! QG
Analysis: System Evolution
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Advanced SynopticM. D. Eastin The BASIC QG Height Tendency
Equation: Term C:Vertical Derivative of Geostrophic Temperature
Advection (Differential Thermal Advection) Important: You should
evaluate the vertical structure of temperature advection!!! QG
Analysis: System Evolution N-S Cross-section of Temperature
Advection WAA = Warm Colors CAA = Cool Colors
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Advanced SynopticM. D. Eastin The BASIC QG Omega Equation:
Application Tips: Remember the underlying assumptions!!! You must
consider the effects of both Term B and Term C at multiple
levels!!! If the vorticity maxima/minima are not collocated with
trough/ridge axes, then Term B will contribute to system intensity
change and motion If the vorticity advection patterns change with
height, expect the system tilt to change with time (become more
tilted or more stacked) If differential temperature advection is
large (small), then expect Term C to produce large (small) changes
in system intensity Opposing expectations from the two terms at a
given location will weaken the total vertical motion (and
complicate the interpretation)!!! The QG height-tendency equation
is a prognostic equation: Can be used to predict the future pattern
of geopotential heights Diagnose the synopticscale contribution to
the height field evolution Predict the formation, movement, and
evolution of synoptic waves QG Analysis: System Evolution
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Advanced SynopticM. D. Eastin References Bluestein, H. B, 1993:
Synoptic-Dynamic Meteorology in Midlatitudes. Volume I: Principles
of Kinematics and Dynamics. Oxford University Press, New York, 431
pp. Bluestein, H. B, 1993: Synoptic-Dynamic Meteorology in
Midlatitudes. Volume II: Observations and Theory of Weather
Systems. Oxford University Press, New York, 594 pp. Charney, J. G.,
B. Gilchrist, and F. G. Shuman, 1956: The prediction of general
quasi-geostrophic motions. J. Meteor., 13, 489-499. Durran, D. R.,
and L. W. Snellman, 1987: The diagnosis of synoptic-scale vertical
motionin an operational environment. Weather and Forecasting, 2,
17-31. Hoskins, B. J., I. Draghici, and H. C. Davis, 1978: A new
look at the equation. Quart. J. Roy. Meteor. Soc., 104, 31-38.
Hoskins, B. J., and M. A. Pedder, 1980: The diagnosis of middle
latitude synoptic development. Quart. J. Roy. Meteor. Soc., 104,
31-38. Lackmann, G., 2011: Mid-latitude Synoptic Meteorology
Dynamics, Analysis and Forecasting, AMS, 343 pp. Trenberth, K. E.,
1978: On the interpretation of the diagnostic quasi-geostrophic
omega equation. Mon. Wea. Rev., 106, 131-137.